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A real polynomial P is said to be stable if all its roots lie in the left half-plane. The term "stable" is used to describe such a polynomial because, in the theory of linear ...

An n-dimensional vector, i.e., a vector (x_1, x_2, ..., x_n) with n components. In dimensions n greater than or equal to two, vectors are sometimes considered synonymous with ...

Any pair of equations giving the real part of a function as an integral of its imaginary part and the imaginary part as an integral of its real part. Dispersion relationships ...

The regulator of a number field K is a positive number associated with K. The regulator of an imaginary quadratic field is 1 and that of a real quadratic, imaginary cubic, or ...

A square root of x is a number r such that r^2=x. When written in the form x^(1/2) or especially sqrt(x), the square root of x may also be called the radical or surd. The ...

If a subgroup H of G has a group representation phi:H×W->W, then there is a unique induced representation of G on a vector space V. The original space W is contained in V, ...

A subset {v_1,...,v_k} of a vector space V, with the inner product <,>, is called orthogonal if <v_i,v_j>=0 when i!=j. That is, the vectors are mutually perpendicular. Note ...

The absolute square of a complex number z, also known as the squared norm, is defined as |z|^2=zz^_, (1) where z^_ denotes the complex conjugate of z and |z| is the complex ...

A square matrix A is called diagonally dominant if |A_(ii)|>=sum_(j!=i)|A_(ij)| for all i. A is called strictly diagonally dominant if |A_(ii)|>sum_(j!=i)|A_(ij)| for all i. ...

An irrational number x can be called GK-regular (defined here for the first time) if the distribution of its continued fraction coefficients is the Gauss-Kuzmin distribution. ...